एक (a+b) भुजा वाले वर्ग में यदि (a) वाली पट्टी और (b) वाली पट्टी की चौड़ाइयाँ बदल दी जाएँ पर कुल भुजा वही रहे, तो कौन-सा क्षेत्रफल संबंध अपरिवर्तित रहेगा?
In a square of side (a+b), if the widths of the (a) strip and (b) strip are interchanged but the total side remains the same, which area relation remains unchanged?
#area-model
#rearrangement
#binomial-square
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A ( (a+b)2 =a-2 +2ab+b-2 )
B ( (a-b)2 =a-2 -2ab+b-2 )
C ( a-2 -b-2 =(a-b)2 )
D ( (a+b)2 =a-2 +b-2 )
Explanation opens after your attempt
Correct Answer
A. ( (a+b)2 =a-2 +2ab+b-2 )
Step 1
Concept
Changing the order of parts does not change total area. In exams, treat rearrangement as equal area.
Step 2
Why this answer is correct
The correct answer is A. ( (a+b)2 =a-2 +2ab+b-2 ). Changing the order of parts does not change total area. In exams, treat rearrangement as equal area.
Step 3
Exam Tip
भागों का क्रम बदलने से कुल क्षेत्रफल नहीं बदलता। परीक्षा में पुनर्व्यवस्था को समान क्षेत्रफल मानें।
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एक वर्ग मॉडल में \(x^2\), दो समान आयत और (49) का कोना है। यदि पूरे वर्ग की भुजा (x+7) है तो दोनों आयतों का संयुक्त क्षेत्रफल क्या होगा?
A square model has \(x^2\), two equal rectangles and a corner (49). If the whole square has side (x+7), what is the combined area of the two rectangles?
#strips
#visual-square
#identity
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A (7x)
B (14x)
C (49x)
D \(x^2+49\)
Explanation opens after your attempt
Step 1
Concept
The two rectangles are (7x) and (7x), so the total is (14x). In exams, count both equal strips.
Step 2
Why this answer is correct
The correct answer is B. (14x). The two rectangles are (7x) and (7x), so the total is (14x). In exams, count both equal strips.
Step 3
Exam Tip
दोनों आयत (7x) और (7x) हैं, इसलिए कुल (14x) है। परीक्षा में दोनों समान पट्टियाँ गिनें।
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यदि (p+q) भुजा वाले वर्ग में (pq) क्षेत्रफल वाले आयतों को तिरछे कोनों पर रखा जाए, तो उनकी कुल संख्या कितनी होगी?
If rectangles of area (pq) are placed at opposite positions in a square of side (p+q), how many such rectangles will be present?
#visual-count
#area-parts
#identity
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A (1)
B (3)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
A (p+q) square forms two (pq) rectangles. In exams, remember the visual source of (2pq).
Step 2
Why this answer is correct
The correct answer is C. (2). A (p+q) square forms two (pq) rectangles. In exams, remember the visual source of (2pq).
Step 3
Exam Tip
(p+q) वर्ग में (pq) के दो आयत बनते हैं। परीक्षा में (2pq) का दृश्य स्रोत याद रखें।
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एक मॉडल में \(m^2+18m+81\) को वर्ग के रूप में दिखाया गया है। किस भुजा से यह मॉडल बनेगा?
A model shows \(m^2+18m+81\) as a square. Which side will form this model?
#perfect-square
#reverse-area
#visual
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A (m+6)
B (m-9 )
C (m+18)
D (m+9)
Explanation opens after your attempt
Step 1
Concept
\(81=9^2\) and \(18m=2\cdot m\cdot9\). In exams, identify the side using the square root of the corner.
Step 2
Why this answer is correct
The correct answer is D. (m+9). \(81=9^2\) and \(18m=2\cdot m\cdot9\). In exams, identify the side using the square root of the corner.
Step 3
Exam Tip
\(81=9^2\) और \(18m=2\cdot m\cdot9\) है। परीक्षा में कोने के वर्गमूल से भुजा पहचानें।
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एक दृश्य मॉडल में बड़ा वर्ग \(16y^2\) है और छोटा जोड़ा गया वर्ग (25) है। यदि दो पट्टियाँ घटाई गई हैं, तो सही क्षेत्रफल कौन-सा है?
In a visual model, the large square is \(16y^2\) and the small added square is (25). If two strips are subtracted, which area is correct?
#subtraction-model
#perfect-square
#visual
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A \(16y^2-40y+25\)
B \(16y^2+40y+25\)
C \(4y^2-20y+25\)
D \(16y^2-20y+25\)
Explanation opens after your attempt
Correct Answer
A. \(16y^2-40y+25\)
Step 1
Concept
The side parts are (4y) and (5), so the subtracted middle term is \(2\cdot4y\cdot5=40y\). In exams, use square roots to form strips.
Step 2
Why this answer is correct
The correct answer is A. \(16y^2-40y+25\). The side parts are (4y) and (5), so the subtracted middle term is \(2\cdot4y\cdot5=40y\). In exams, use square roots to form strips.
Step 3
Exam Tip
भुजाएँ (4y) और (5) हैं, इसलिए बीच का घटा पद \(2\cdot4y\cdot5=40y\) है। परीक्षा में वर्गमूल लेकर पट्टियाँ बनाएं।
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एक आयत मॉडल में (r+11) और (r-11) को साथ रखा गया है। दृश्य रूप से कौन-से रैखिक भाग कटेंगे?
In a rectangle model, (r+11) and (r-11) are placed together. Which linear parts cancel visually?
#cancellation
#difference-of-squares
#visual
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A (11r) और (11r) / (11r) and (11r)
B (11r) और (-11r) / (11r) and (-11r)
C \(r^2\) और (-121) / \(r^2\) and (-121)
D (121) और (-121) / (121) and (-121)
Explanation opens after your attempt
Correct Answer
B. (11r) और (-11r) / (11r) and (-11r)
Step 1
Concept
Positive (11r) and negative (11r) cancel because their areas are equal. In exams, look for equal rectangles with opposite signs.
Step 2
Why this answer is correct
The correct answer is B. (11r) और (-11r) / (11r) and (-11r). Positive (11r) and negative (11r) cancel because their areas are equal. In exams, look for equal rectangles with opposite signs.
Step 3
Exam Tip
धनात्मक (11r) और ऋणात्मक (11r) बराबर क्षेत्रफल के कारण कटते हैं। परीक्षा में विपरीत चिन्ह वाले समान आयत देखें।
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यदि (3x+4) और (3x-4) के आयत मॉडल में (3x) भाग को वर्ग माना जाए, तो बचा क्षेत्रफल क्या होगा?
If in the rectangle model of (3x+4) and (3x-4), the (3x) part is treated as the square side, what area remains?
#difference-of-squares
#rectangle
#expert
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A \(9x^2+16\)
B \(3x^2-16\)
C \(9x^2-16\)
D \(9x^2-24x+16\)
Explanation opens after your attempt
Correct Answer
C. \(9x^2-16\)
Step 1
Concept
This is the visual model of ( (3x)2 -42 ). In exams, square both terms separately.
Step 2
Why this answer is correct
The correct answer is C. \(9x^2-16\). This is the visual model of ( (3x)2 -42 ). In exams, square both terms separately.
Step 3
Exam Tip
यह ( (3x)2 -42 ) का दृश्य मॉडल है। परीक्षा में दोनों पदों का वर्ग अलग-अलग करें।
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एक टाइल व्यवस्था \(x^2+15x+54\) को आयत बनाती है। किन स्थिर पट्टियों से यह व्यवस्था संभव है?
A tile arrangement \(x^2+15x+54\) forms a rectangle. Which constant strips make this arrangement possible?
#area-tiles
#factorisation
#visual
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A (2) और (27) / (2) and (27)
B (5) और (10) / (5) and (10)
C (3) और (18) / (3) and (18)
D (6) और (9) / (6) and (9)
Explanation opens after your attempt
Correct Answer
D. (6) और (9) / (6) and (9)
Step 1
Concept
(6+9=15) and \(6\times9=54\). In exams, match both sum and product.
Step 2
Why this answer is correct
The correct answer is D. (6) और (9) / (6) and (9). (6+9=15) and \(6\times9=54\). In exams, match both sum and product.
Step 3
Exam Tip
(6+9=15) और \(6\times9=54\) है। परीक्षा में योग और गुणनफल दोनों मिलाएँ।
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एक वर्ग मॉडल में \(25a^2+60a+36\) है। छोटे कोने की भुजा और बड़े भाग की भुजा क्रमशः क्या हैं?
A square model has \(25a^2+60a+36\). What are the side of the small corner and the side of the large part respectively?
#reverse-square
#side-length
#visual
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A (6) और (5a) / (6) and (5a)
B (5a) और (6) / (5a) and (6)
C (36) और (25a) / (36) and (25a)
D (3) और (10a) / (3) and (10a)
Explanation opens after your attempt
Correct Answer
A. (6) और (5a) / (6) and (5a)
Step 1
Concept
The small corner is \(36=6^2\) and the large square is (25a-2 =(5a)2 ). In exams, derive side lengths from areas.
Step 2
Why this answer is correct
The correct answer is A. (6) और (5a) / (6) and (5a). The small corner is \(36=6^2\) and the large square is (25a-2 =(5a)2 ). In exams, derive side lengths from areas.
Step 3
Exam Tip
छोटा कोना \(36=6^2\) और बड़ा वर्ग (25a-2 =(5a)2 ) है। परीक्षा में क्षेत्रफल से भुजा निकालें।
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यदि (a+b+c) भुजा वाले वर्ग को तीन भागों में काटकर मॉडल बनाया जाए, तो (ab) प्रकार के कितने आयत होंगे?
If a square of side (a+b+c) is cut into three parts to make a model, how many rectangles of type (ab) will appear?
#three-term-square
#area-count
#visual
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
(ab) and (ba) appear as two different rectangles. In exams, count each pair twice.
Step 2
Why this answer is correct
The correct answer is B. (2). (ab) and (ba) appear as two different rectangles. In exams, count each pair twice.
Step 3
Exam Tip
(ab) और (ba) दो अलग आयतों में दिखते हैं। परीक्षा में हर जोड़ी को दो बार गिनें।
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एक (u+v+w) वर्ग मॉडल में कुल मिश्रित आयतों का क्षेत्रफल कौन-सा होगा?
In a square model of (u+v+w), what will be the total area of the mixed rectangles?
#mixed-rectangles
#three-term-identity
#visual
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A (uv+vw+wu)
B \(u^2+v^2+w^2\)
C (2uv+2vw+2wu)
D (3uvw)
Explanation opens after your attempt
Correct Answer
C. (2uv+2vw+2wu)
Step 1
Concept
Each mixed pair appears in two rectangles. In exams, multiply all three pairs by (2).
Step 2
Why this answer is correct
The correct answer is C. (2uv+2vw+2wu). Each mixed pair appears in two rectangles. In exams, multiply all three pairs by (2).
Step 3
Exam Tip
हर मिश्रित जोड़ी दो आयतों में आती है। परीक्षा में तीनों जोड़ियों को (2) से गुणा करें।
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यदि किसी मॉडल में \(x^2\), (8x), (15x) और (120) भाग हैं, तो आयत की संभावित भुजाएँ कौन-सी हैं?
If a model has parts \(x^2\), (8x), (15x) and (120), what are the possible sides of the rectangle?
#rectangle-model
#area-parts
#factor-form
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A (x+5) और (x+24) / (x+5) and (x+24)
B (x+23) और (x+120) / (x+23) and (x+120)
C (x+10) और (x+12) / (x+10) and (x+12)
D (x+8) और (x+15) / (x+8) and (x+15)
Explanation opens after your attempt
Correct Answer
D. (x+8) और (x+15) / (x+8) and (x+15)
Step 1
Concept
The two linear strips are (8x) and (15x), and the corner is \(8\times15=120\). In exams, read sides from the linear strips.
Step 2
Why this answer is correct
The correct answer is D. (x+8) और (x+15) / (x+8) and (x+15). The two linear strips are (8x) and (15x), and the corner is \(8\times15=120\). In exams, read sides from the linear strips.
Step 3
Exam Tip
दो रैखिक पट्टियाँ (8x) और (15x) हैं और कोना \(8\times15=120\) है। परीक्षा में रैखिक पट्टियों से भुजाएँ पढ़ें।
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एक छात्र ने ( (2x+3)2 ) के मॉडल में मध्य पद (6x) लिखा। सही दृश्य सुधार क्या है?
A student wrote the middle term (6x) in the model of ( (2x+3)2 ). What is the correct visual correction?
#error-analysis
#visual-square
#middle-term
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A दो (6x) पट्टियाँ जोड़ें / Add two (6x) strips
B एक (6x) पट्टी हटाएँ / Remove one (6x) strip
C (3x) कोना जोड़ें / Add a (3x) corner
D \(4x^2\) हटाएँ / Remove \(4x^2\)
Explanation opens after your attempt
Correct Answer
A. दो (6x) पट्टियाँ जोड़ें / Add two (6x) strips
Step 1
Concept
The model has two (2x) by (3) rectangles, so the middle term is (12x). In exams, do not stop at one strip.
Step 2
Why this answer is correct
The correct answer is A. दो (6x) पट्टियाँ जोड़ें / Add two (6x) strips. The model has two (2x) by (3) rectangles, so the middle term is (12x). In exams, do not stop at one strip.
Step 3
Exam Tip
मॉडल में दो (2x) गुणा (3) आयत होते हैं, इसलिए मध्य पद (12x) है। परीक्षा में एक पट्टी पर नहीं रुकें।
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एक (5t-2) भुजा वाले वर्ग में घटाई गई दो पट्टियों का कुल क्षेत्रफल कितना है?
In a square of side (5t-2), what is the total area of the two subtracted strips?
#subtracted-strips
#minus-square
#area
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A (10t)
B (20t)
C \(25t^2\)
D (4)
Explanation opens after your attempt
Step 1
Concept
The two strips are \(5t\cdot2\) and \(5t\cdot2\), so total (20t) is subtracted. In exams, include both strips.
Step 2
Why this answer is correct
The correct answer is B. (20t). The two strips are \(5t\cdot2\) and \(5t\cdot2\), so total (20t) is subtracted. In exams, include both strips.
Step 3
Exam Tip
दो पट्टियाँ \(5t\cdot2\) और \(5t\cdot2\) हैं, इसलिए कुल (20t) घटता है। परीक्षा में दोनों पट्टियाँ शामिल करें।
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यदि (x+12) वर्ग मॉडल में \(x^2\) और (144) कोना दिया है, तो कौन-सा भाग मॉडल को पूरा करेगा?
If a square model of (x+12) gives \(x^2\) and a corner (144), which part will complete the model?
#complete-model
#binomial-square
#visual
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A (12x) की एक पट्टी / One strip of (12x)
B (144x) का संयुक्त पट्टी क्षेत्रफल / Combined strip area of (144x)
C (24x) का संयुक्त पट्टी क्षेत्रफल / Combined strip area of (24x)
D \(x^2+144\) की अतिरिक्त परत / Extra layer of \(x^2+144\)
Explanation opens after your attempt
Correct Answer
C. (24x) का संयुक्त पट्टी क्षेत्रफल / Combined strip area of (24x)
Step 1
Concept
Both strips are (12x). In exams, add two side strips along with the corner.
Step 2
Why this answer is correct
The correct answer is C. (24x) का संयुक्त पट्टी क्षेत्रफल / Combined strip area of (24x). Both strips are (12x). In exams, add two side strips along with the corner.
Step 3
Exam Tip
दोनों पट्टियाँ (12x) की होती हैं। परीक्षा में कोने के साथ दो साइड पट्टियाँ जोड़ें।
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एक आयत मॉडल में (2a+5) और (a-3) हैं। चार भागों को जोड़कर सही क्षेत्रफल कौन-सा है?
A rectangle model has (2a+5) and (a-3). Which area is correct after adding the four parts?
#signed-area
#rectangle-model
#expansion
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A \(2a^2+2a-15\)
B \(2a^2+11a-15\)
C \(2a^2-6a+5\)
D \(2a^2-a-15\)
Explanation opens after your attempt
Correct Answer
D. \(2a^2-a-15\)
Step 1
Concept
The parts are \(2a^2\), (-6a), (5a) and (-15), so the linear term is (-a). In exams, add negative rectangles correctly.
Step 2
Why this answer is correct
The correct answer is D. \(2a^2-a-15\). The parts are \(2a^2\), (-6a), (5a) and (-15), so the linear term is (-a). In exams, add negative rectangles correctly.
Step 3
Exam Tip
भाग \(2a^2\), (-6a), (5a) और (-15) हैं, इसलिए रैखिक पद (-a) है। परीक्षा में ऋण आयतों को सही जोड़ें।
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एक क्षेत्रफल मॉडल में धनात्मक टाइल (12x) और ऋणात्मक टाइल (-5x) एक साथ हैं। संयुक्त रैखिक क्षेत्रफल क्या होगा?
In an area model, a positive tile (12x) and a negative tile (-5x) are together. What is the combined linear area?
#signed-tiles
#linear-term
#visual
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A (7x)
B (17x)
C (-7x)
D \(60x^2\)
Explanation opens after your attempt
Step 1
Concept
Positive and negative tiles leave a difference of (7x). In exams, treat signed tiles as algebraic addition.
Step 2
Why this answer is correct
The correct answer is A. (7x). Positive and negative tiles leave a difference of (7x). In exams, treat signed tiles as algebraic addition.
Step 3
Exam Tip
धनात्मक और ऋणात्मक टाइलों का अंतर (7x) बचाता है। परीक्षा में चिह्नित टाइलों को बीजगणितीय जोड़ की तरह लें।
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यदि ( (x-4)(x+9) ) को चिह्नित टाइल मॉडल से फैलाया जाए, तो कौन-सा स्थिर कोना मिलेगा?
If ( (x-4)(x+9) ) is expanded by a signed tile model, what constant corner is obtained?
#signed-area
#constant-term
#rectangle
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A (36)
B (-36)
C (13)
D (-13)
Explanation opens after your attempt
Step 1
Concept
The constant part is ((-4)\cdot9=-36). In exams, unlike signs create a negative corner.
Step 2
Why this answer is correct
The correct answer is B. (-36). The constant part is ((-4)\cdot9=-36). In exams, unlike signs create a negative corner.
Step 3
Exam Tip
स्थिर भाग ((-4)\cdot9=-36) है। परीक्षा में अलग चिन्हों के गुणन से ऋणात्मक कोना बनता है।
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एक मॉडल \(x^2+5x-36\) को आयत में बदलता है। कौन-सी भुजाएँ सही हैं?
A model changes \(x^2+5x-36\) into a rectangle. Which sides are correct?
#factorisation
#signed-tiles
#visual
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A (x+12) और (x-3) / (x+12) and (x-3)
B (x+6) और (x-6) / (x+6) and (x-6)
C (x+9) और (x-4) / (x+9) and (x-4)
D (x-9) और (x+4) / (x-9) and (x+4)
Explanation opens after your attempt
Correct Answer
C. (x+9) और (x-4) / (x+9) and (x-4)
Step 1
Concept
(9+(-4)=5) and (9\cdot(-4)=-36). In exams, check signs in both sum and product.
Step 2
Why this answer is correct
The correct answer is C. (x+9) और (x-4) / (x+9) and (x-4). (9+(-4)=5) and (9\cdot(-4)=-36). In exams, check signs in both sum and product.
Step 3
Exam Tip
(9+(-4)=5) और (9\cdot(-4)=-36) है। परीक्षा में योग और गुणनफल में चिन्ह जाँचें।
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यदि \(y^2-14y+49\) का दृश्य वर्ग मॉडल बने, तो हटाई गई प्रत्येक पट्टी का क्षेत्रफल क्या होगा?
If \(y^2-14y+49\) is shown as a visual square model, what is the area of each removed strip?
#removed-strip
#perfect-square
#visual
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A \(y^2\)
B (14y)
C (49y)
D (7y)
Explanation opens after your attempt
Step 1
Concept
The total removed strips are (14y), so each is (7y). In exams, divide the middle term into two equal parts.
Step 2
Why this answer is correct
The correct answer is D. (7y). The total removed strips are (14y), so each is (7y). In exams, divide the middle term into two equal parts.
Step 3
Exam Tip
कुल हटाई गई पट्टियाँ (14y) हैं, इसलिए प्रत्येक (7y) है। परीक्षा में कुल मध्य पद को दो बराबर भागों में बाँटें।
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एक (2m+3n) भुजा वाले वर्ग में दोनों मिश्रित आयतों का संयुक्त क्षेत्रफल क्या होगा?
In a square of side (2m+3n), what will be the combined area of the two mixed rectangles?
#mixed-rectangle
#binomial-square
#visual
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A (12mn)
B (6mn)
C \(4m^2+9n^2\)
D (5mn)
Explanation opens after your attempt
Step 1
Concept
One mixed rectangle is \(2m\cdot3n=6mn\), and there are two such rectangles. In exams, double the mixed rectangles.
Step 2
Why this answer is correct
The correct answer is A. (12mn). One mixed rectangle is \(2m\cdot3n=6mn\), and there are two such rectangles. In exams, double the mixed rectangles.
Step 3
Exam Tip
एक मिश्रित आयत \(2m\cdot3n=6mn\) है और ऐसे दो आयत होते हैं। परीक्षा में मिश्रित आयतों को दोगुना करें।
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यदि (3a-2b) भुजा वाले वर्ग का मॉडल बनाया जाए, तो अंतिम विस्तार कौन-सा है?
If a model is made for a square of side (3a-2b), which final expansion is correct?
#binomial-square
#coefficients
#visual
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A \(9a^2-6ab+4b^2\)
B \(9a^2-12ab+4b^2\)
C \(3a^2-12ab+2b^2\)
D \(9a^2+12ab+4b^2\)
Explanation opens after your attempt
Correct Answer
B. \(9a^2-12ab+4b^2\)
Step 1
Concept
The subtracted middle term is \(2\cdot3a\cdot2b=12ab\). In exams, include both coefficients.
Step 2
Why this answer is correct
The correct answer is B. \(9a^2-12ab+4b^2\). The subtracted middle term is \(2\cdot3a\cdot2b=12ab\). In exams, include both coefficients.
Step 3
Exam Tip
बीच का घटा पद \(2\cdot3a\cdot2b=12ab\) है। परीक्षा में दोनों गुणांकों को शामिल करें।
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एक आयत का मॉडल \(4x^2-25y^2\) को दिखाता है। इसे कौन-सी भुजाएँ बना सकती हैं?
A rectangle model shows \(4x^2-25y^2\). Which sides can form it?
#difference-of-squares
#conjugate-sides
#visual
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A (2x+25y) और (2x-5y) / (2x+25y) and (2x-5y)
B (4x+25y) और (4x-25y) / (4x+25y) and (4x-25y)
C (2x+5y) और (2x-5y) / (2x+5y) and (2x-5y)
D (x+5y) और (x-5y) / (x+5y) and (x-5y)
Explanation opens after your attempt
Correct Answer
C. (2x+5y) और (2x-5y) / (2x+5y) and (2x-5y)
Step 1
Concept
(4x-2 =(2x)2 ) and (25y-2 =(5y)2 ). In exams, write difference of squares as two conjugate sides.
Step 2
Why this answer is correct
The correct answer is C. (2x+5y) और (2x-5y) / (2x+5y) and (2x-5y). (4x-2 =(2x)2 ) and (25y-2 =(5y)2 ). In exams, write difference of squares as two conjugate sides.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और (25y-2 =(5y)2 ) है। परीक्षा में वर्गों के अंतर को दो संयुग्म भुजाओं में लिखें।
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एक दृश्य प्रमाण में ( (a+b)2 -(a-b)2 ) को चार समान आयतों में पुनर्व्यवस्थित किया गया। प्रत्येक आयत का क्षेत्रफल क्या है?
In a visual proof, ( (a+b)2 -(a-b)2 ) is rearranged into four equal rectangles. What is the area of each rectangle?
#visual-proof
#area-difference
#rearrangement
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A (4ab)
B (2ab)
C \(a^2-b^2\)
D (ab)
Explanation opens after your attempt
Step 1
Concept
The total difference is (4ab), so each of the four equal rectangles is (ab). In exams, divide total area into equal parts.
Step 2
Why this answer is correct
The correct answer is D. (ab). The total difference is (4ab), so each of the four equal rectangles is (ab). In exams, divide total area into equal parts.
Step 3
Exam Tip
कुल अंतर (4ab) है, इसलिए चार समान आयतों में प्रत्येक (ab) होगा। परीक्षा में कुल क्षेत्रफल को समान भागों में बाँटें।
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यदि ( (x+y+z)2 ) के क्षेत्रफल मॉडल में केवल वर्गों का योग घटा दिया जाए, तो क्या बचेगा?
If the sum of only the squares is removed from the area model of ( (x+y+z)2 ), what remains?
#three-term-square
#mixed-area
#visual
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A (2xy+2yz+2zx)
B (xy+yz+zx)
C (x+y+z)
D (3xyz)
Explanation opens after your attempt
Correct Answer
A. (2xy+2yz+2zx)
Step 1
Concept
After removing the squares, only six mixed rectangles remain. In exams, add them as (2xy+2yz+2zx).
Step 2
Why this answer is correct
The correct answer is A. (2xy+2yz+2zx). After removing the squares, only six mixed rectangles remain. In exams, add them as (2xy+2yz+2zx).
Step 3
Exam Tip
वर्ग हटाने पर केवल छह मिश्रित आयत बचते हैं। परीक्षा में उन्हें (2xy+2yz+2zx) के रूप में जोड़ें।
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एक (a+b) वर्ग मॉडल में यदि \(a^2+b^2\) को विकर्ण के पास रखा गया है, तो शेष दो भागों का कुल क्षेत्रफल क्या है?
In a square model of (a+b), if \(a^2+b^2\) is placed near the diagonal, what is the total area of the remaining two parts?
#diagonal-layout
#area-parts
#visual
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A (ab)
B (2ab)
C \(a^2-b^2\)
D (2a+2b)
Explanation opens after your attempt
Step 1
Concept
The remaining two rectangles are (ab) and (ab). In exams, add the rectangles left after the squares.
Step 2
Why this answer is correct
The correct answer is B. (2ab). The remaining two rectangles are (ab) and (ab). In exams, add the rectangles left after the squares.
Step 3
Exam Tip
शेष दो आयत (ab) और (ab) हैं। परीक्षा में वर्गों के अतिरिक्त बचे आयतों को जोड़ें।
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यदि ( (a+b)2 ) और \(a^2+b^2\) के मॉडलों में क्षेत्रफल का अंतर पूछा जाए, तो सही अंतर क्या है?
If the area difference between the models of ( (a+b)2 ) and \(a^2+b^2\) is asked, what is the correct difference?
#area-difference
#binomial-square
#visual
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A (ab)
B (a+b)
C (2ab)
D \(a^2-b^2\)
Explanation opens after your attempt
Step 1
Concept
( (a+b)2 ) has two extra (ab) rectangles along with \(a^2+b^2\). In exams, view the difference as missing rectangles.
Step 2
Why this answer is correct
The correct answer is C. (2ab). ( (a+b)2 ) has two extra (ab) rectangles along with \(a^2+b^2\). In exams, view the difference as missing rectangles.
Step 3
Exam Tip
( (a+b)2 ) में \(a^2+b^2\) के साथ दो (ab) आयत अतिरिक्त होते हैं। परीक्षा में अंतर को छूटे आयतों से देखें।
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एक मॉडल में ( (2x+1)2 -(2x-1)2 ) के दो वर्गों का अंतर दिखाया गया। परिणाम क्या होगा?
A model shows the difference of two squares ( (2x+1)2 -(2x-1)2 ). What is the result?
#square-difference
#visual-proof
#identity
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A (4x)
B (2x)
C \(4x^2-1\)
D (8x)
Explanation opens after your attempt
Step 1
Concept
On subtracting the two expansions, (4x-(-4x)=8x) remains. In exams, take the difference of opposite middle terms.
Step 2
Why this answer is correct
The correct answer is D. (8x). On subtracting the two expansions, (4x-(-4x)=8x) remains. In exams, take the difference of opposite middle terms.
Step 3
Exam Tip
दोनों विस्तार घटाने पर (4x-(-4x)=8x) बचता है। परीक्षा में विपरीत मध्य पदों का अंतर लें।
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यदि (x+4) और (x-2) की चिह्नित आयत टाइलों में (x) वाले कुल टाइल कितने क्षेत्रफल के बराबर होंगे?
In signed rectangle tiles for (x+4) and (x-2), what will be the total area of the (x)-tiles?
#signed-rectangle
#linear-area
#visual
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A (2x)
B (6x)
C (-2x)
D (-8x)
Explanation opens after your attempt
Step 1
Concept
The linear tiles are (4x) and (-2x), so the total is (2x). In exams, add signed linear tiles.
Step 2
Why this answer is correct
The correct answer is A. (2x). The linear tiles are (4x) and (-2x), so the total is (2x). In exams, add signed linear tiles.
Step 3
Exam Tip
रैखिक टाइल (4x) और (-2x) हैं, इसलिए कुल (2x) है। परीक्षा में चिह्नित रैखिक टाइलों को जोड़ें।
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एक मॉडल \(2x^2+7x+3\) को आयत में बदलता है। कौन-सा विभाजन सही दृश्य निर्माण देता है?
A model converts \(2x^2+7x+3\) into a rectangle. Which split gives the correct visual construction?
#area-factorisation
#split-middle
#visual
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A \(2x^2+2x+5x+3\)
B \(2x^2+x+6x+3\)
C \(2x^2+3x+4x+3\)
D \(2x^2+7x+7+3\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+x+6x+3\)
Step 1
Concept
\(1\cdot6=6\) and \(2\cdot3=6\), so grouping (x+6x) gives ((2x+1)(x+3)). In exams, verify the middle split by area grouping.
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+x+6x+3\). \(1\cdot6=6\) and \(2\cdot3=6\), so grouping (x+6x) gives ((2x+1)(x+3)). In exams, verify the middle split by area grouping.
Step 3
Exam Tip
\(1\cdot6=6\) और \(2\cdot3=6\), इसलिए (x+6x) समूह से ((2x+1)(x+3)) बनता है। परीक्षा में मध्य पद विभाजन को क्षेत्रफल समूह से जाँचें।
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यदि \(3x^2+10x+3\) का टाइल मॉडल गुणनखंड आयत बनाता है, तो सही भुजाएँ कौन-सी हैं?
If the tile model of \(3x^2+10x+3\) forms a factor rectangle, which sides are correct?
#factor-rectangle
#area-tiles
#quadratic
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A (3x+10) और (x+3) / (3x+10) and (x+3)
B (3x+3) और (x+1) / (3x+3) and (x+1)
C (3x+1) और (x+3) / (3x+1) and (x+3)
D (x+1) और (x+9) / (x+1) and (x+9)
Explanation opens after your attempt
Correct Answer
C. (3x+1) और (x+3) / (3x+1) and (x+3)
Step 1
Concept
These sides give parts \(3x^2\), (9x), (x) and (3). In exams, check by adding all four parts.
Step 2
Why this answer is correct
The correct answer is C. (3x+1) और (x+3) / (3x+1) and (x+3). These sides give parts \(3x^2\), (9x), (x) and (3). In exams, check by adding all four parts.
Step 3
Exam Tip
इन भुजाओं से भाग \(3x^2\), (9x), (x) और (3) मिलते हैं। परीक्षा में चारों भागों को जोड़कर जाँचें।
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एक दृश्य मॉडल में ( (x+6)2 ) से ( (x+2)2 ) घटाया गया। बचा क्षेत्रफल किसके बराबर है?
In a visual model, ( (x+2)2 ) is subtracted from ( (x+6)2 ). What is the remaining area equal to?
#difference-of-square-models
#visual
#area
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A (4x+16)
B (4x+32)
C (8x+16)
D (8x+32)
Explanation opens after your attempt
Correct Answer
D. (8x+32)
Step 1
Concept
The difference is ((x+6+x+2)(x+6-x-2)= (2x+8)\cdot4=8x+32). In exams, use difference of squares.
Step 2
Why this answer is correct
The correct answer is D. (8x+32). The difference is ((x+6+x+2)(x+6-x-2)= (2x+8)\cdot4=8x+32). In exams, use difference of squares.
Step 3
Exam Tip
अंतर ((x+6+x+2)(x+6-x-2)= (2x+8)\cdot4=8x+32) है। परीक्षा में वर्गों के अंतर का उपयोग करें।
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यदि बाहरी वर्ग की भुजा (x+5) और अंदर का वर्ग (x-1) हो, तो सीमा पट्टी का क्षेत्रफल क्या होगा?
If the outer square has side (x+5) and the inner square has side (x-1), what is the border area?
#border-area
#visual-difference
#squares
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A (12x+24)
B (8x+24)
C (6x+24)
D (10x+25)
Explanation opens after your attempt
Correct Answer
A. (12x+24)
Step 1
Concept
The area difference is ((x+5)2 -(x-1)2 =12x+24). In exams, subtract inner square from outer square.
Step 2
Why this answer is correct
The correct answer is A. (12x+24). The area difference is ((x+5)2 -(x-1)2 =12x+24). In exams, subtract inner square from outer square.
Step 3
Exam Tip
क्षेत्रफल अंतर ((x+5)2 -(x-1)2 =12x+24) है। परीक्षा में बाहरी और अंदरूनी वर्ग का अंतर लें।
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एक (a+b) वर्ग को चार भागों में काटकर आयत में बदला गया। यदि आयत की एक भुजा (a+b) ही रहती है, तो दूसरी भुजा क्या रहेगी?
A square of (a+b) is cut into four parts and changed into a rectangle. If one side of the rectangle remains (a+b), what will the other side be?
#rearrangement
#equal-area
#square
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A (a-b)
B (a+b)
C (2a+2b)
D (ab)
Explanation opens after your attempt
Step 1
Concept
Area is unchanged and one side is unchanged, so the other side is also (a+b). In exams, infer using equal area and equal side.
Step 2
Why this answer is correct
The correct answer is B. (a+b). Area is unchanged and one side is unchanged, so the other side is also (a+b). In exams, infer using equal area and equal side.
Step 3
Exam Tip
क्षेत्रफल समान और एक भुजा समान है, इसलिए दूसरी भुजा भी (a+b) होगी। परीक्षा में समान क्षेत्रफल और समान भुजा से निष्कर्ष निकालें।
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एक (x+3) वर्ग मॉडल में \(x^2\) और (9) को अलग रंग दिया गया। यदि रंगहीन क्षेत्र (30) है, तो (x) का मान क्या होगा?
In a square model of (x+3), \(x^2\) and (9) are colored separately. If the uncolored area is (30), what is the value of (x)?
#unknown-value
#visual-square
#area
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The uncolored area is two (3x) strips, so (6x=30) and (x=5). In exams, connect uncolored strips to the middle term.
Step 2
Why this answer is correct
The correct answer is C. (5). The uncolored area is two (3x) strips, so (6x=30) and (x=5). In exams, connect uncolored strips to the middle term.
Step 3
Exam Tip
रंगहीन क्षेत्र दो (3x) पट्टियाँ हैं, इसलिए (6x=30) और (x=5)। परीक्षा में रंगहीन पट्टियों को मध्य पद से जोड़ें।
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यदि (x-4) वर्ग मॉडल में वापस जोड़ा गया कोना (16) है और अंतिम क्षेत्रफल (81) है, तो (x) का धनात्मक मान क्या होगा?
If in a square model of (x-4), the added-back corner is (16) and final area is (81), what is the positive value of (x)?
#unknown-side
#subtraction-model
#visual
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A (5)
B (9)
C (17)
D (13)
Explanation opens after your attempt
Step 1
Concept
From ((x-4)2 =81), (x-4=9) and (x=13). In exams, treat the side as a positive length.
Step 2
Why this answer is correct
The correct answer is D. (13). From ((x-4)2 =81), (x-4=9) and (x=13). In exams, treat the side as a positive length.
Step 3
Exam Tip
((x-4)2 =81) से (x-4=9) और (x=13) मिलता है। परीक्षा में भुजा को धनात्मक लंबाई मानें।
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एक आयत मॉडल में (x+2) और (x+5) की जगह (x+3) और (x+4) रख दिए गए। दोनों क्षेत्रों में क्या अंतर है?
In a rectangle model, (x+2) and (x+5) are replaced by (x+3) and (x+4). What is the difference between the two areas?
#compare-rectangles
#area-model
#identity
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A (1)
B (0)
C (x)
D (2x)
Explanation opens after your attempt
Step 1
Concept
The first area is \(x^2+7x+10\) and the second is \(x^2+7x+12\). In exams, when linear terms match, compare constants.
Step 2
Why this answer is correct
The correct answer is A. (1). The first area is \(x^2+7x+10\) and the second is \(x^2+7x+12\). In exams, when linear terms match, compare constants.
Step 3
Exam Tip
पहला क्षेत्र \(x^2+7x+10\) और दूसरा \(x^2+7x+12\) है। परीक्षा में समान रैखिक पद होने पर स्थिर अंतर देखें।
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एक दृश्य प्रमाण में ( (a+b)(c+d) ) को चार छोटे आयतों में बाँटा गया। सही विभाजन कौन-सा है?
In a visual proof, ( (a+b)(c+d) ) is divided into four small rectangles. Which decomposition is correct?
#distributive-area
#rectangle-decomposition
#visual
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A (ab+cd+ac+bd)
B (ac+ad+bc+bd)
C \(a^2+b^2+c^2+d^2\)
D (abcd)
Explanation opens after your attempt
Correct Answer
B. (ac+ad+bc+bd)
Step 1
Concept
Each small rectangle is made from one part of each side. In exams, multiply row by column.
Step 2
Why this answer is correct
The correct answer is B. (ac+ad+bc+bd). Each small rectangle is made from one part of each side. In exams, multiply row by column.
Step 3
Exam Tip
हर छोटे आयत की भुजाएँ एक-एक भाग से बनती हैं। परीक्षा में पंक्ति और स्तंभ का गुणन करें।
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यदि ( (x+2)(x+8) ) और ( (x+5)2 ) के क्षेत्रफल मॉडलों की तुलना हो, तो कौन बड़ा है और कितना?
If area models of ( (x+2)(x+8) ) and ( (x+5)2 ) are compared, which is larger and by how much?
#compare-area-models
#perfect-square
#rectangle
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A ( (x+2)(x+8) ), (9) से / ( (x+2)(x+8) ), by (9)
B दोनों बराबर / Both are equal
C ( (x+5)2 ), (9) से / ( (x+5)2 ), by (9)
D ( (x+5)2 ), (3x) से / ( (x+5)2 ), by (3x)
Explanation opens after your attempt
Correct Answer
C. ( (x+5)2 ), (9) से / ( (x+5)2 ), by (9)
Step 1
Concept
( (x+5)2 =x-2 +10x+25 ) and ( (x+2)(x+8)=x-2 +10x+16 ). In exams, cancel equal (x) terms and compare constants.
Step 2
Why this answer is correct
The correct answer is C. ( (x+5)2 ), (9) से / ( (x+5)2 ), by (9). ( (x+5)2 =x-2 +10x+25 ) and ( (x+2)(x+8)=x-2 +10x+16 ). In exams, cancel equal (x) terms and compare constants.
Step 3
Exam Tip
( (x+5)2 =x-2 +10x+25 ) और ( (x+2)(x+8)=x-2 +10x+16 ) है। परीक्षा में समान (x) पदों को काटकर स्थिर भाग तुलना करें।
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एक जाली मॉडल में कुल क्षेत्रफल \(x^2+2kx+k^2\) है। यह कब पूर्ण वर्ग का दृश्य मॉडल होगा?
A grid model has total area \(x^2+2kx+k^2\). When will it be a visual model of a perfect square?
#general-model
#perfect-square
#visual
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A कभी नहीं / Never
B केवल जब (k=0) / Only when (k=0)
C केवल जब (x=k) / Only when (x=k)
D हमेशा, भुजा (x+k) / Always, side (x+k)
Explanation opens after your attempt
Correct Answer
D. हमेशा, भुजा (x+k) / Always, side (x+k)
Step 1
Concept
It directly shows the four parts of ( (x+k)2 ). In exams, view (2kx) as two (kx) strips.
Step 2
Why this answer is correct
The correct answer is D. हमेशा, भुजा (x+k) / Always, side (x+k). It directly shows the four parts of ( (x+k)2 ). In exams, view (2kx) as two (kx) strips.
Step 3
Exam Tip
यह सीधे ( (x+k)2 ) के चार भाग दिखाता है। परीक्षा में (2kx) को दो (kx) पट्टियों के रूप में देखें।
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यदि \(x^2-2kx+k^2\) को घटाव वाले वर्ग मॉडल से बनाया गया है, तो भुजा क्या होगी?
If \(x^2-2kx+k^2\) is made by a subtraction square model, what will be the side?
#general-minus-square
#visual-model
#identity
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A (x-k)
B (x+k)
C (2x-k)
D (x-2k)
Explanation opens after your attempt
Step 1
Concept
Two (kx) strips are subtracted and the \(k^2\) corner is added back. In exams, identify (x-k) from (-2kx).
Step 2
Why this answer is correct
The correct answer is A. (x-k). Two (kx) strips are subtracted and the \(k^2\) corner is added back. In exams, identify (x-k) from (-2kx).
Step 3
Exam Tip
दो (kx) पट्टियाँ घटती हैं और \(k^2\) कोना वापस जुड़ता है। परीक्षा में (-2kx) से (x-k) पहचानें।
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एक (x+y) वर्ग मॉडल में यदि दो (xy) आयतों को मिलाकर एक लंबा आयत बनाया जाए, तो उसका क्षेत्रफल क्या होगा?
In a square model of (x+y), if two (xy) rectangles are combined into one long rectangle, what is its area?
#rearranged-rectangles
#area-conservation
#visual
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A (xy)
B (2xy)
C \(x^2+y^2\)
D (2x+2y)
Explanation opens after your attempt
Step 1
Concept
Combining two equal rectangles gives (2xy). In exams, rearrangement does not change area.
Step 2
Why this answer is correct
The correct answer is B. (2xy). Combining two equal rectangles gives (2xy). In exams, rearrangement does not change area.
Step 3
Exam Tip
दो समान आयतों को जोड़ने से (2xy) बनता है। परीक्षा में पुनर्व्यवस्था से क्षेत्रफल नहीं बदलता।
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यदि ( (a+b+c)2 ) के दृश्य मॉडल में \(a^2+b^2+c^2\) और (2ab+2bc) दिख रहा है, तो कौन-सा भाग छूटा है?
If the model of ( (a+b+c)2 ) shows \(a^2+b^2+c^2\) and (2ab+2bc), which part is missing?
#missing-part
#three-term-square
#visual
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A (ab+bc+ca)
B (abc)
C (2ca)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 2
Why this answer is correct
The correct answer is C. (2ca). Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 3
Exam Tip
तीन मिश्रित जोड़ियों में (ca) जोड़ी भी दो बार आती है। परीक्षा में सभी जोड़ी संयोजन पूरे करें।
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एक मॉडल में ( (x+4)2 ) से (16) कोना हटाया गया पर पट्टियाँ रखी गईं। शेष क्षेत्रफल क्या है?
In a model, the (16) corner is removed from ( (x+4)2 ) but the strips are kept. What is the remaining area?
#corner-removed
#square-model
#area
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A (8x+16)
B \(x^2+4x\)
C \(x^2+16\)
D \(x^2+8x\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+8x\)
Step 1
Concept
( (x+4)2 =x-2 +8x+16 ), so removing the corner leaves \(x^2+8x\). In exams, subtract the removed part.
Step 2
Why this answer is correct
The correct answer is D. \(x^2+8x\). ( (x+4)2 =x-2 +8x+16 ), so removing the corner leaves \(x^2+8x\). In exams, subtract the removed part.
Step 3
Exam Tip
( (x+4)2 =x-2 +8x+16 ), कोना हटाने पर \(x^2+8x\) बचता है। परीक्षा में हटाए गए भाग को घटाएँ।
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यदि ( (2x+7)2 ) के दृश्य मॉडल में \(4x^2\) और (49) पहले से हैं, तो छूटा पट्टी क्षेत्रफल क्या है?
If in the visual model of ( (2x+7)2 ), \(4x^2\) and (49) are already present, what is the missing strip area?
#missing-strips
#coefficient-square
#visual
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A (28x)
B (14x)
C (7x)
D (21x)
Explanation opens after your attempt
Step 1
Concept
The total of two mixed rectangles is \(2\cdot2x\cdot7=28x\). In exams, find middle area with coefficients.
Step 2
Why this answer is correct
The correct answer is A. (28x). The total of two mixed rectangles is \(2\cdot2x\cdot7=28x\). In exams, find middle area with coefficients.
Step 3
Exam Tip
दो मिश्रित आयतों का कुल \(2\cdot2x\cdot7=28x\) है। परीक्षा में गुणांक सहित मध्य क्षेत्रफल निकालें।
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एक आयत मॉडल ( (x-5)(x-7) ) के लिए चिह्नित टाइलें बनाता है। मध्य पद का दृश्य अर्थ क्या है?
A rectangle model forms signed tiles for ( (x-5)(x-7) ). What is the visual meaning of the middle term?
#signed-tiles
#negative-strips
#rectangle
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A दो धनात्मक पट्टियाँ (12x) / Two positive strips (12x)
B दो ऋणात्मक पट्टियों का कुल (-12x) / Total (-12x) from two negative strips
C एक धनात्मक कोना (35x) / One positive corner (35x)
D दो विपरीत पट्टियाँ जो कट जाती हैं / Two opposite strips that cancel
Explanation opens after your attempt
Correct Answer
B. दो ऋणात्मक पट्टियों का कुल (-12x) / Total (-12x) from two negative strips
Step 1
Concept
The linear parts are (-5x) and (-7x), whose sum is (-12x). In exams, add both negative strips.
Step 2
Why this answer is correct
The correct answer is B. दो ऋणात्मक पट्टियों का कुल (-12x) / Total (-12x) from two negative strips. The linear parts are (-5x) and (-7x), whose sum is (-12x). In exams, add both negative strips.
Step 3
Exam Tip
रैखिक भाग (-5x) और (-7x) हैं, जिनका योग (-12x) है। परीक्षा में दोनों ऋणात्मक पट्टियाँ जोड़ें।
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यदि \(x^2-12x+35\) की टाइलों से आयत बने, तो कौन-सी भुजाएँ मॉडल को सही बनाती हैं?
If tiles of \(x^2-12x+35\) form a rectangle, which sides make the model correct?
#signed-factorisation
#area-tiles
#visual
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A (x-1) और (x-35) / (x-1) and (x-35)
B (x+5) और (x+7) / (x+5) and (x+7)
C (x-5) और (x-7) / (x-5) and (x-7)
D (x+12) और (x-35) / (x+12) and (x-35)
Explanation opens after your attempt
Correct Answer
C. (x-5) और (x-7) / (x-5) and (x-7)
Step 1
Concept
(-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 2
Why this answer is correct
The correct answer is C. (x-5) और (x-7) / (x-5) and (x-7). (-5+(-7)=-12) and ((-5)(-7)=35). In exams, product of two negative constants is positive.
Step 3
Exam Tip
(-5+(-7)=-12) और ((-5)(-7)=35) है। परीक्षा में दो ऋणात्मक स्थिर भागों का गुणन धनात्मक होता है।
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एक (a-b) वर्ग मॉडल में \(a^2\) से दो (ab) पट्टियाँ हटाने के बाद कौन-सी त्रुटि हो सकती है?
In a square model of (a-b), after removing two (ab) strips from \(a^2\), what error may occur?
#common-error
#subtraction-square
#visual
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A (a+b) को भुजा मानना / Taking (a+b) as the side
B \(a^2\) को दो बार जोड़ना / Adding \(a^2\) twice
C (ab) को धनात्मक रखना / Keeping (ab) positive
D \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back
Explanation opens after your attempt
Correct Answer
D. \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back
Step 1
Concept
The corner \(b^2\) is removed twice, so it must be added back. In exams, correct over-subtraction.
Step 2
Why this answer is correct
The correct answer is D. \(b^2\) को वापस न जोड़ना / Not adding \(b^2\) back. The corner \(b^2\) is removed twice, so it must be added back. In exams, correct over-subtraction.
Step 3
Exam Tip
कोने का \(b^2\) भाग दो बार हट जाता है, इसलिए उसे वापस जोड़ना जरूरी है। परीक्षा में अधिक घटाव ठीक करें।
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यदि दो वर्गों की भुजाएँ (x+k) और (x-k) हों, तो उनके क्षेत्रफल मॉडलों का अंतर किसके बराबर होगा?
If two squares have sides (x+k) and (x-k), what will the difference of their area models be?
#difference-of-area-models
#general-identity
#visual
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A (4kx)
B (2kx)
C \(x^2-k^2\)
D \(2x^2+2k^2\)
Explanation opens after your attempt
Step 1
Concept
The difference of expansions is (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx). In exams, cancel equal square terms.
Step 2
Why this answer is correct
The correct answer is A. (4kx). The difference of expansions is (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx). In exams, cancel equal square terms.
Step 3
Exam Tip
विस्तारों का अंतर (x-2 +2kx+k-2 -\(x^2-2kx+k^2\)=4kx) है। परीक्षा में समान वर्ग पद काटें।
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एक दृश्य मॉडल में ( (x+a)(x+b) ) का क्षेत्रफल और ( \(x+\frac{a+b}{2}\)2 ) का क्षेत्रफल तुलना किया गया। दूसरा क्षेत्र पहले से कितना अधिक है?
A visual model compares the area of ( (x+a)(x+b) ) and ( \(x+\frac{a+b}{2}\)2 ). How much greater is the second area than the first?
#advanced-comparison
#visual-area
#identity
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A \( \frac{a+b}{2} \)
B ( \frac{(a-b)2 }{4} )
C ( ab )
D \( \frac{a^2+b^2}{2} \)
Explanation opens after your attempt
Correct Answer
B. ( \frac{(a-b)2 }{4} )
Step 1
Concept
Both have (x-2 +(a+b)x) common, and the constant difference is ( \frac{(a+b)2 }{4}-ab=\frac{(a-b)2 }{4} ). In exams, remove common parts and compare remaining area.
Step 2
Why this answer is correct
The correct answer is B. ( \frac{(a-b)2 }{4} ). Both have (x-2 +(a+b)x) common, and the constant difference is ( \frac{(a+b)2 }{4}-ab=\frac{(a-b)2 }{4} ). In exams, remove common parts and compare remaining area.
Step 3
Exam Tip
दोनों में (x-2 +(a+b)x) समान है, स्थिर भागों का अंतर ( \frac{(a+b)2 }{4}-ab=\frac{(a-b)2 }{4} ) है। परीक्षा में समान भाग हटाकर बचा क्षेत्रफल देखें।
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